SOLUTION: write a conjecture that describes the pattern. Then use your conjecture to find the next two terms in the sequence -2,4,-8,16,-32

-2,4,-8,16,-32

Twice -2 is -4, change the sign to get the next term 4

Twice 4 is 8, change the sign to get the next term -8

Twice -8 is -16, change the sign to get the next term 16

Twice 16 is 32, change the sign to get the next term -32

Therefore we can continue with the same pattern:

Twice -32 is -64, change the sign to 64.  That's the next term.

Twice 64 is 128, change the sign to get the next term -128

So the next two terms were 64 and -128.


So the pattern is:

Start with -2

To get the next term, multiply by 2 and change the sign

(Or you could say, start with -2 and to get the next term 
each time multiply the preceding term by -2.)


Edwin